微分对策中的有限时间局部捕捉区

本文继续用文献1,2]中"有限时间局部捕捉区"的概念,分析"双目标微分对策"(或角 色二重性)问题,并得到下列新结果:较文献1,2]更详尽地分析了奇异曲面,分别对于左、右 两半目标集得到更为完整的局部捕捉区;得出在捕捉区及"危险区"内控制(u,v)的划分区 域;由局部捕捉区可确定任意点处的"捕捉时间";找出"互相格杀"的区域;讨论了参数变化的 影响. 由这些结果可以看出,用"有限时间局部捕捉区"的概念,解这类问题是有效的,亦可能用 来解其它有关问题.

The Partial Capture Region on Finite time Interval in Differential Games

In this paper, as a subsequent work of 1, 2] , the idea of "partial capture region on finite time interval" and the method in 1, 2] are used to solve the two-target differential game (or role ambiguity problem). The following new results are obtained, the singular surfaces are analysed in more details than that in 2] and the partial capture regions are constructed more completely for the right and left half target set; both the capture and "danger" regions are divided into several subregions for different (u. v); for any state the "time to go" can be determined by the partial capture regions; the region of "simultaneous kill" is obtained; the effects of altering parameters are discussed. These results show that our method is effective, and it can be used to solve some other relevant problems.